State officials have said they would ease restrictions when the average for new daily cases over a two-week window falls below five.
"So this is "gold standard", apparently, according to the Federal Government".
Passengers from New Zealand arrive at Sydney International Airport on Friday.
"I can confirm that there are 65 people that have travelled from New Zealand and ultimately arrived in Victoria".
But the Victorian government has said it did not expect to receive worldwide travellers as a result of New South Wales making a travel bubble arrangement with New Zealand.
They urged Andrews to speed up the reopening of businesses, particularly in the restaurant and hospitality sector, which they said was losing 1,000 jobs every day of the lockdown.
"We would prefer better management of these arrangements but this is something that happened that was outside of our control", Western Australia Premier Mark McGowan said on Sunday.
"We will just make sure we provide the best advice we can and we will try to get the most contemporary and the most accurate information out of border force as it relates to people that are coming and we will try to take the best care of them that we possibly can".
Deputy Prime Minister Michael McCormack disagreed with Andrews, saying in an interview each of the Australian states were responsible for their own borders.
"The Victorian government was present when it was discussed, they were made aware that this was going to occur, they raised no objections in the meetings", he said.
"I think it is completely unreasonable, completely unreasonable to be putting it to me that somehow it's my fault or the Victorian Government's fault, that when you are invited to participate in an arrangement and you say no, that somehow people turn up".
In response to Mr Tudge's statement, Professor Sutton said he had attended the meeting in question but was not present for the trans-Tasman bubble discussion.
"If you are travelling from New Zealand and have passed all relevant immigration and biosecurity requirements as established by the Federal Government, NSW Government and Northern Territory Government, then you are able to travel to Victoria", the website states.
Melbourne residents are expecting COVID-19 restrictions to be eased on Sunday but it is unclear how much freedom will be regained.
"The Federal Government when times get tough, just wash their hands of any responsibility".
New Zealanders arrive at Sydney airport last week.
The outbreak in Victoria came after other parts of Australia had successfully contained the epidemic and begun to reopen their economies, notably in neighbouring New South Wales, which includes Sydney.
Another 23 of the bubble travellers flew onto Perth, which does have restrictions on visitors from other Australian states, so the 22 adults involved are in hotel isolation in Perth, and one child is with a family member in Perth.
Australians are now unable to travel to New Zealand under the same conditions.